1946 年,物理学家 Stanislaw Ulam 在洛斯阿拉莫斯国家实验室研究核武器的项目中,提出了现代版本的马尔可夫链蒙特卡洛方法(Markov Chain Monte Carlo, MCMC),以代替传统的确定性数值算法。并且 Ulam 与同事 von Neumann,Metropolis 提议将这一绝密计划的代号命名为 Monte Carlo,这来源于他那经常借钱赌博的叔叔常去的...
Corollary: If P has a limiting distribution π , then every row of Pt converges to π . TIME REVERSIBILITY Time reversibility drives almost any Markov Chain Monte Carlo algorithm. We will define the concept using the stationary distribution of the chain, which we shall show that is meaningful....
Introduction to Markov chain Monte Carlo ( MCMC ) and its role in modern Bayesian analysisGregory, Phil
We also comment on how the convergence of a Markov chain to equilibrium can be assessed in practice and provide an illustrating example. Finally, we review some of the freely available, existing software for implementing MCMC methods. Keywords: Monte Carlo simulation; Markov chains; Bayesian ...
1. An Introduction to MCMC 15 Markov chain Monte Carlo (MCMC) algorithms are now widely used in virtually all areas of statistics. In particular, spatial applications featured very prominently in the early development of the methodology (Geman & Geman 1984), and they still provide some of the...
Understanding the concept of Markov Chains Now, let’s break down the above statements one by one and define a Markov Chain really means. We will start with the third statement and then gradually move to the first one. Any random process is known to have the Markov property if the probabil...
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov chain, Metropolis algorithm, continuous phase transition, statistical...
point processes - Moller, Waagepetersen - 2002 () Citation Context ...cesses have concentrated on parameter estimation based on maximum pseudo likelihood estimation [1, 5, 13] or approximate maximum likelihood estimation using Markov chain Monte Carlo (MCMC) algorithms =-=[9, 10, 18, 19]-=...
First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting...
Markov Chain Monte Carlo (HMCMC).Using Bayesian inference is the provably best method of combining data with domain knowledge to extract interpretable and insightful results that lead us towards better outcomes. In my opinion, this is what students need to learn to be clear-thinking and capable ...